The queueing probability (and queueing time) under scaling regimes has also been studied in load-balancing models, where each server has its own queue, and where each arriving job is immediately dispatched to a server upon arrival. The Join-the-Idle-Queue (JIQ) policy routes every arriving job to an idle queue, if one exists, otherwise to a randomly selected queue [1]}, [2]}. For JIQ it was shown that diminishing queueing probability can be achieved when the load, \(\rho ^{(n)}\) , is lighter than \(1- \frac{1}{n}\)  [3]}, [4]}, [5]}. Another example is the Power-of-\(d\) -Choices policy (Po\(d\) ), where every arriving job samples \(d\)  queues and goes to the shortest of these [6]}, [7]}. For Po\(d\)  it was shown that diminishing queueing probability can be achieved when \(d=\Omega \left(\frac{\log n}{1-\rho ^{(n)}}\right)\)  in the sub-Halfin-Whitt regime and when \(d=\Omega \left(\frac{\log ^2n}{1-\rho ^{(n)}}\right)\)  for \(\rho ^{(n)}\)  lighter than \(1- \frac{1}{n}\)  [3]}, [4]}, [10]}.
Moreover, the Join-the-Shortest-Queue (JSQ) load-balancing policy can be viewed as a special case of Po\(d\) , where \(d=n\) . Thus it too has diminishing queueing probability.
Finally, [11]} extend the traditional load-balancing model to address data locality and again prove diminishing queueing probability under specific conditions on the data locality.
